The "visual mastering" thing is marketing spin. I have some intention of toning it down in the future but I've got more important things to worry about than monkeying around with marketing spiel.
"Eyes to the ears" is a more realistic slogan that I like. It does not mean give way to your eyes if your ears tell you everything you need. More the case that when you are struggling to hear what is wrong (but you know something is wrong) it can give visual insight. We don't suggest you simply trust what you see and go by that. Its an interactive process of listening and seeing and experimenting with changes. The key word here is "experimenting".
You might see a large whole in the spectrum and wonder is that bad acoustics or phase cancellation or simply a result of the instrumentation in the track. To answer the question you dive in and make some changes and listen to the effect. Did it improve? Yes, then perhaps we have phase cancellation issues in the mix, No, then it is a natural signature of the track instrumentation. That is essentially how I use it. I never know with certainty, apriori, whether a track spectrum clearly demonstrates a particular issue. I may have strong suspicions but they are only confirmed after adjustment and listening.
IntuitQ and IntuitMatch are merely tools for the user that is unwilling to experiment and does not have monitoring that they can trust. However, if you want to make good sounding recordings you should try and get monitoring you can trust. In the case of speakers most of that is the room more than the speakers, though good speakers are important.
How can you know if you can reasonably trust your monitoring? I would say the easiest way would be to invest in some decent quality headphones and compare the tonality of what you hear in the headphones with what you hear in the room. If there is a general consistency then you can, if not, then your monitor may be biased one way or the other.
Then it's a matter of treating your room until you come up with something comparable. Now don't read too much into this because I'm not saying they should sound the same as they won't. Speakers should sound spatially richer that headphones as you have the room ambiance (hopefully) adding to the performance. The imaging in headphones is also totally different, but that does not mean you can't have comparable tonal balance and that is the consistency I'm referring too.
So in summary, yes, you need to trust what you hear and if you don't have faith in your monitoring then you should probably look and rectifying that. If nothing else, use good quality headphones to judge tonality and speakers for imaging.